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1、4-1 Chapter 4 Multiple Regression: Estimation and Hypothesis Testing 主主讲讲：李李宗宗璋璋 Email: Email: Lizongzhang9Lizongzhang9 TEL: 189TEL: 189- -28862886- -13561356 OFFICE: OFFICE: 经经管管学学院院812812室室 华华南南农农业业学学经经管管理理学学院院会会计计系系 4-2 4.1 The three-variable linear regression model 12233 12233 12233 : ( ) : iii
2、iiii iiii PRF E YBB XB X YBB XB Xu SRF Ybb Xb Xe =+ =+ =+ 4-3 12233iiii YBB XB Xu=+ nY can be expressed as the sum of two components: nA systematic or deterministic component nNonsystematic or random component 12233ii BB XB X+ i u 4-4 偏偏回回归归系系数数 nPartial Regression Coefficient: nP153. 4-5 4.2 Assump
3、tions of Multiple Linear Regression Model (3.1 The Classical Linear Regression Model) The CLRM makes the following assumptions: nA4.1=A3.1: Linear +A3.6 : Correct model specification n A4.2=A3.2 :The explanatory variable is uncorrelated with the disturbance term. n A4.3=A3.3 : The expected value of
4、the disturbance term is zero. n A4.4=A3.4 : Homoscedastic nA4.5 =A3.5 : No autocorrelation between two error terms. 4-6 4.2 Assumptions of Multiple Linear Regression Model A4.6 No collinearity 解解释释变变量量之之间间不不存存在在完完全全共共线线性性 Chap 8 多多重重共共线线性性的的后后果果 A4.7=A3.7 the error term u follows the normal distribu
5、tion 4-7 4.3 Estimation of Parameters of Multiple Regression nOLS Estimators () 2 2 12233 123 ( ,) iiii RSSeYbb Xb X f b b b =- = 4-8 Estimation of Parameters of Multiple Regression 4-9 OLS Estimators 4-10 Simple Linear: OLS Estimators 4-11 4.4 Multiple Coefficient of Determination 多元判定系数 2 ESS R TS
6、S = 4-12 多元相关系数 Coefficient of multiple correlation Y与与所所有有解解释释变变量量的的线线性性相相关关程程度度。 2 RR= 4-13 4.7 Testing hypotheses about individual partial regression coefficients. nT-test：二元回归中单个参数的t检验 4-14 回归模型中单个参数的假设检验 n 检验统计量： * () ( ) : : ii i bB tt nk se b k n - =-: 模型中待估参数的个数 样本容量 4-15 4.7 Testing hypothe
7、ses about individual partial regression coefficients. The Test of Significance Approach The Confidence Interval Approach 4-16 4.8 Testing the joint hypothesis 联合假设检验 nJoint hypothesis 多多元元回回归归的的总总体体显显著著性性检检验验 Test of the overall significance of the estimated multiple regression 所所有有的的斜斜率率系系数数同同时时为为0
8、 0， 没没有有包包括括截截距距系系数数！ 4-17 两个解释变量各自对应变量没有影响，但却 联合对应变量有影响。 202 023 303 :0 :0 :0 2Y 23Y 3Y HB HBB HB X XX X = = = 不拒绝 不拒绝 不拒绝 单独对 没有显著影响 不能得出：和联合起来对 没有显著影响 单独对 没有显著影响 4-18 回归模型的总体（整体）显著性检验 Test of the overall significance of the regression 023 123 2 0 2 1 :0 :,0 :0 :0 k k HBBB HB BB HR HR = = 不同时为 or：
9、 所所有有的的斜斜率率系系数数同同时时为为0 0， 没没有有包包括括截截距距系系数数！ 4-19 F-test : : k n 模型中待估参数的个数 样本容量 4-20 Table 4-1 ANOVA ANOVA table for the three-variable regression. 4-21 F-test 023 :0HBB= F值值越越大大，解解释释变变量量对对应应变变量量的的变变异异解解释释能能力力越越大大。 4-22 Table 4-2 ANOVA table for the clock auction price example. 4-23 An Important Rel
10、ationship Between F & R- square 2 2 (1) (1) () R k F R nk - = - - 4-24 An Important Relationship Between F & R- square 2 2 /(1) /() /(1) /(1) /() (1)/() ESSk F RSSnk ESSk Rk TSS RSSnk Rnk TSS - = - - - = - - 4-25 Table 4-3 ANOVA table in terms of R2. 4-26 一元回归中t-test & F-test等价 2 020 2 12 1 :0:0 :0
11、:0 HBHR HB HR = 4-27 一元回归中t-test & F-test等价 4-28 4.9 Specification Error 8-52 PRICE = -191.666193 + 10.48562272*AGE 8-53 PRICE = 807.9501188 + 54.57244656*NOBIDDERS 8-37 PRICE = -1336.049287 + 12.74138352*AGE + 85.76406701*NOBIDDERS 4-29 4-52 4-30 4-53 4-31 4-37 4-32 4.10 The Adjusted R-square 22 1
12、1 (1) n AdjustedRR nk - -= - - 4-33 4.11 When to add an additional explanatory variable to the Model n如果增加变量系数的t值绝对值大于1，则 adjusted R2将增加 4-34 Table 4-4 A comparison of four models of antique clock auction prices. 4-35 4.12 Restricted Least Sqares 受受约约束束最最小小二二乘乘 表表8-4 Model3: 受受限限模模型型，限限制制条条件件：Age的的系
13、系数数为为0 2 2 3:807.9501 54.5724 0.1549 4:1336.049 12.741385.7640 0.8906 r ur ModelYBidders R ModelYAgeBidders R =+ = = -+ = 22 urr RR 4-36 0 1 22 2 :RestrictedModel :UnrestrictedModel ()/ F (1)/() urr ur H H RRm Rnk - = - 限制条件成立， 限制条件不成立， m: 限限制制条条件件的的个个数数 K:无无约约束束回回归归中中的的参参数数个个数数 4-37 一元回归还是二元回归？ 0 1
14、 22 , 2 0 :Model3 B0 :Model4 B0 ()/ F (1)/() (0.89060.1549)/10.7357 F194.116 (1 0.8906)/(323)0.00379 0.000 age age urr m n k ur Hrestricted Hunrestricted RRm F Rnk pvalue rejectH - = - = - - = - -= 4-38 13.965372=194.116 4-39 Table 4-5 Leverage in manufacturing corporations, 1935-1982. 4-40 Table 4-
15、6 Child mortality, fertility, and related data for 64 countries. 4-41 Figure 4A-1 Normal probability plot for Example 8.4. AD = Anderson-Darling Statistic. 4-42 Figure 4A-4 Eviews output of the clock auction price example. 4-43 第第四四章章重重点点 n多多元元回回归归模模型型中中增增加加的的假假定定：不不完完全全共共线线性性 n多多元元回回归归中中单单个个参参数数的的假
16、假设设检检验验 n多多元元回回归归的的整整体体显显著著性性检检验验 n多多元元回回归归的的差差分分析析表表 n校校正正的的R2R2 n受受限限最最小小乘乘：F testF test 4-44 Exercise 讨论：母的教育程度对新的体重是否有显著 影响？ = (+ *cigs+parity+,faminc +-motheduc+.fatheduc+u Ref: Wooldridge (2015) Introductory Econometrics, A modern approach, example 4.9 4-45 Restricted OLS: F test (: Restricted model = (+ *cigs+parity+,faminc+u *:
